{
  "id": "1004.1751",
  "version": "v1",
  "published": "2010-04-10T23:14:17.000Z",
  "updated": "2010-04-10T23:14:17.000Z",
  "title": "Limit sets and commensurability of Kleinian groups",
  "authors": [
    "Wen-yuan Yang",
    "Yue-ping Jiang"
  ],
  "comment": "9 pages",
  "journal": "Bulletin of the Australian Mathematical Society (2010), 82:1-9",
  "doi": "10.1017/S0004972710000146",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "In this paper, we obtain several results on the commensurability of two Kleinian groups and their limit sets. We prove that two finitely generated subgroups $G_1$ and $G_2$ of an infinite co-volume Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ having $\\Lambda(G_1) = \\Lambda(G_2)$ are commensurable. In particular, it is proved that any finitely generated subgroup $H$ of a Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ with $\\Lambda(H) = \\Lambda(G)$ is of finite index if and only if $H$ is not a virtually fiber subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-10T23:14:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40"
    ],
    "keywords": [
      "limit sets",
      "commensurability",
      "infinite co-volume kleinian group",
      "finitely generated subgroup",
      "finite index"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1751Y"
    }
  }
}